The Physics of the Trampoline Effect in Baseball and Softball Bats

In the high-speed collision between a baseball and bat, most of the initial center-of-mass kinetic energy is converted into compressional energy in the ball, and about 75% of that energy is dissipated. Some of the energy is stored in vibrational modes of the bat, particularly in the so-called “hoop modes”, the most important of which is a radial deformation with a quadrupole azimuthal dependence. The lowest such mode has a frequency in the 1-3 kHz range and is strongly excited during the collision by the local compression of the shell of the bat at the point of impact. Some of the collision energy that would otherwise have been stored and mostly dissipated in the ball is stored in this mode. Interestingly and for reasons examined in this paper, much of this stored energy is returned to the ball, resulting in less overall energy dissipated and a correspondingly larger ball exit speed. This is popularly called the "trampoline effect", and the goal of this paper is to examine the physics behind the effect. A simple picture of the trampoline effect is presented and the consequences of this picture are interpreted in physical terms. Results of a more realistic model are given, along with comparisons with data. Finally a discussion of whether “corking” a wood bat produces a trampoline effect is presented.